How Many Samples do I Need? Part 3

1
How Many Samples do I Need?Part 3
DQO Training Course Day 1 Module 6

• Presenter Sebastian Tindall

(50 minutes)(5 minute stretch break)
2
Sampling for Environmental Activities

• Chuck RamseyEnviroStat, Inc.PO Box 636Fort
  Collins, CO 80522970-689-5700970-229-9977 fax
• chuck_at_envirostat.org
• www.envirostat.org

3
Seven Major Sampling Errors

• Fundamental Error - FE
• Grouping and Segregation Error - GSE
• Materialization Error - ME
• Delimination Error - DE
• Extraction Error - EE
• Preparation Error - PE
• Trends - CE2
• Cycles - CE3

4
Ramseys Rules

• All measurements are an average
• With discreet sampling, an average is a random
  variable
• With discreet sampling, SD is an artifact of the
  sample collection process
• Heterogeneity is the rule
• Multi-increment sampling can drive a skewed
  distribution towards normal
• FE2
• proportional to particle size
• inversely proportional to mass
• Lab data are suspect (error can be large)

5
Ramseys Rules (cont.)

• Good sampling technique is critical
• Typical sample sizes will underestimate the mean
• Quality control (QC) is important
• NO boiler plate (e.g., PARCC)
• QC must be problem specific
• Maximize the use of onsite analysis to guide
  planning decisions
• DQOs are the most important component of the
  process

6
Ramseys Rules (cont.)

• One measurement is a crap shoot
• Tremendous heterogeneity (variability) between
• Particles within a sample
• Aliquots of a sample
• Duplicate samples
• Never take ONE grab sample to base a decision
• Always collect X increments and use AT LEAST one
  multi-increment sample to make the decision

7
Multi-Increment Sampling is the Way to Go
Next following slides show How to perform
multi-increment sampling
8
Multi-Increment Sampling
n m k 100 1 100 100 2
50 100 4 25 100 5 20 100
10 10 n number of samples required k
increments m samples analyzed
9
n m k
Collect n samples
Group into k increments
k 3
k 3
Remember we want the AVERAGE over the Decision
Unit
Combine k into m multi- increments
m 2
FAM/Laboratory
10
Comparison of Discrete vs. Multi-Increment

• Remember (In discreet sampling)
• An average is a random variable
• The SD is an artifact of the sample collection
  process.

11
Average Exposure

• In discreet sampling, the sample mean is a random
  variable.
• In discreet sampling, the 95 UCL is a random
  variable.
• In discreet sampling, the sample standard
  deviation is an artifact of sample collection
  process.
• n ( samples) is NOT proportional to the size of
  the population (e.g. area, mass, or volume).

12
Average depends on locations sampled
Average A 16 ppm Average B 221 ppm Average
from discrete sampling is a random variable
13
Hot Spots

• 1,000,000 g at site
• 100,000 g gt AL
• Take 10 samples
• 1gt AL
• Remove that 1
• Re-sample clean
• Wrong!
• If 100,000 gtAL
• Minus 1
• Still 99,999gtAL

x
AL action level
14
Hot Spots Simply Means I want to look at units
(e.g. Mass, volume) that are becoming smaller
and smaller and smaller and smaller and
smaller and smaller and smaller

15
Effects of Grinding a Soil
Walsh, Marianne E. Ramsey, Charles A. Jenkins,
Thomas F., The Effect of Particle Size Reduction
by Grinding on Subsampling Variance for
Explosives Residues in Soil, Chemosphere 49
(2002) 1267-1273.
16
Additional Population Considerations

• Sample support - physical size, shape and
  orientation of the material that is extracted
  from the sampling unit that is actually available
  to be measured or observed, and therefore, to
  represent the sampling unit.
• Assure enough sample for analyses
• Specify how the sample support will be processed
  and sub-sampled for analysis.

EPA Guidance on Choosing a Sampling Design for
Environmental Data Collection, EPA QA/G-5S,
December 2002, EPA/240/R-02/005
17
Sub-Sampling

• The DQO must define what represents the
  population in terms of laboratory sample size
• Typical laboratory sample sizes that are digested
  or extracted metals - 1g, volatiles - 5g,
  semi-volatiles - 30 g
• The 1g or 30g sample analyzed by the lab is
  supposed to represent a larger area/mass (e.g.,
  acre). Does it?

18
Fundamental Error
3
d
2

FE
5
.
22

M

• FE fundamental error
• M mass of sample (g)
• d maximum particle size lt5 oversize (cm)

EPA/600/R-92/128, July 1992
19
Fundamental Error
3
d
2
FE

5
.
22

M

• 22.5 clfg
• c - mineralogical factor
• ? - density factor (for soil 2.5)
• l - liberation factor (between 0 -1)
• f - shape factor (for soil 0.5)
• g - granulometric factor 0.25

20
Fundamental Error

• Solve for
• particle size

OR
Solve for mass of sample
21
Constant Particle Size
9217 gm 20 4097 gm 30 Particle Size -
2.54 cm
22
Examples of FE, Mass, Particle Size
23
Examples of FE, Mass, Particle Size

• May not work well or at all with some media
• Clay
• Water
• Air

24
Multi-Increment Sampling is the Way to Go
exposure unit decision unit DU (1)
Lab(7)
Samples QC (6)
calc d FE mass(2,3,4)
10 scoops(5)
Re-Calculate particle size(8)
Sub sample mass for lab analysis(10)
Average concentration for DU(12,13)
Analyze entire sub sample(11)
Grind(9)
25
Multi-Increment Sampling is the Way to Go
1. Agree on exposure unit or decision unit. 2.
Select or measure a reasonable maximum sample
particle size. 3. Select the FE. 4.
Calculate the mass of sample needed based on the
FE and particle size. 5. Using a square
scoop large enough to capture the maximum
particle size, collect enough sample
increments (k) to equal the mass
calculated in 4 and place in a jar, combining
increments into one sample (m). 6.
Repeat within a given decision unit to obtain a
duplicate (or triplicate) to generate the
QC. 7. Deliver the sample and QC sample(s) to
the lab.
26
Multi-Increment Sampling is the Way to Go,
continued
8. Calculate the particle size of sample
needed based on the desired FE and the mass that
the lab normally uses for a given analysis. 9.
Lab must grind entire mass of field sample ( QC)
to the agreed upon maximum analytical particle
size in 8. 10. Lab must perform one-dimensional
sub-sampling of entire mass spread entire ground
sample on flat surface in thin layer, then
systematically or randomly collect sufficient
small mass sub-sampling increments to equal the
mass the laboratory requires for an analysis do
likewise for each QC sample. 11. Combine
sub-sampling increments into the sample, then
digest/extract/analyze the sample and QC
samples. 12. Calculate the concentration from
sample. 13. Concentration represents average
concentration or activity per decision unit.
27
Example

• Soil like material
• Largest particle about 4 mm
• Action limit is 500 ppm
• Analytical aliquot is one gram
• Is this acceptable?

Compliments of EnviroStat, Inc.
28
Example (cont)

• Check particle size representatives

FE 1.2
FE percent 1.2 100
FE percent 120
EPA/600/R-92/128, July 1992
Compliments of EnviroStat, Inc.
29
Example (cont)

• What mass is required to reduce FE to 15?

But lab can analyze 10 grams at the most
Compliments of EnviroStat, Inc.
30
Example (cont)

• To what particle size does the sample need to be
  reduced to achieve FE of 15?

Compliments of EnviroStat, Inc.
31
Example (cont)

• What is the FE to take 64 grams and grind it to
  0.1 cm and take one gram?

Ignoring all the other errors
Compliments of EnviroStat, Inc.
32
Example (cont)

• Option 1
• take at least 64 grams and grind to 0.1 cm
• analyze one gram
• Option 2
• take at least 64 grams and grind to 0.22 cm
• analyze 10 grams
• Other options
• investigate/estimate sampling factors (clfg)

Compliments of EnviroStat, Inc.
33
Multi-increment Sampling

• Saves money
• Results are more defensible
• Does not excite the public
• Faster

34
Key Points

• All measurements are an average
• In discreet sampling, the average is a random
  variable
• In discreet sampling, the SD is an artifact of
  the sample collection process
• Heterogeneity is the rule
• Multi-increment sampling can save your butt!
• Multi-increment sampling can get you defensible
  data within your sampling analyses budget

35
Key Points (cont.)

• Due to inherent heterogeneity, collecting
  representative sample is difficult
• TRIAD approach and Ramseys Rules advocate
• using cheaper, real-time, on-site methods
• increasing sample density or coverage
• Controlling laboratory analysis quality does not
  control all error
• Errors occur in each step of the collection and
  analysis process

36
Key Points (cont.)

• TRIAD approach encourages use of DWP to provide
  flexibility to obtain sufficient sample density
• Larger the mass, the lower the sampling error
• Smaller the particle, the lower the sampling
  error
• Proper sub-sampling is critical
• Sample design must assess the normal, skewed, and
  badly skewed distributions
• For badly skewed computer simulations are needed
• Multi-increment samples drive the distribution to
  normal

37
How Many Samples do I Need?

• REMEMBER

HETEROGENEITY IS THE RULE!
38
Summary

• Use Classical Statistical sampling approach
• Almost certain to fail
• Use Other Statistical sampling approaches
• Bayesian
• Geo-statistics
• Kriging
• Use Multi-Increment sampling approach
• Can use classical statistics
• Cheaper
• Faster
• More defensible

?
MASSIVE DATA Required
39
End of Module 6

• Thank you
• Questions?
• We will now take a
• Second Afternoon 5-minute Stretch Break.
• Please be back in 5 minutes